Rashi in the tractate of Megilla (22b) quotes a Medrash that explains that at the time when the nation of Israel was planning the construction of the Golden Calf, the women were approached and asked to donate their gold jewelry for the cause. The women, realizing that this scheme was totally inappropriate and even sinful, steadfastly refused to give over any of their gold. Because of their firm commitment to Moshe and their faith in G-d which manifested itself in the refusal to hand over their gold and their distance from the sin of the Golden Calf, women were rewarded with having Rosh Chodesh being a special holy day for themselves.

Why specifically was Rosh Chodesh given to women? The Menoras HaMaor explains that each of the three major holidays represents one of our forefathers. Pesach is representative of Avraham, because it was on Pesach that Avraham was informed by the angels that he was going to have a son. Shavuos is representative of Yitzchak because before the Torah was given (which Shavuos comemorates), a shofar made from the ram that was sacrificed instead of Yitzchak was sounded to signal the monumental event. Sukkos is representative of Yaakov because we find in the Torah that Yaakov built booths in a place he named Sukkos. However, the three major holidays are not the only festive occasions which are associated with someone. Originally, the twelve months were representative of and carried significance to each of the twelve tribes. Because the tribes sinned by the incident of the Golden Calf, this "holiday" was taken away from them as a punishment. It was given instead to those who did not involve themselves with this incident, and were therefore deserving of reward: the righteous women of Israel.